Start-up flow of a Bingham fluid between two coaxial cylinders under a constant wall shear stress

The analytical solution of the start-up flow of a Bingham fluid between two co-axial cylinders is presented in this study. We focus on that all fluid is at rest initially, then a constant shear stress is exerted by the inner cylinder while the outer remains stationary. The problem is solved using methods of Laplace transform and numerical integration. The unsteady solutions of shear stress and angular velocity as well as the motion of yielding surface are given. We also conduct the limiting analysis at infinitesimal values of the time after initiation.